David H. Weinberg, James S. Bullock, Fabio Governato, Rachel Kuzio de Naray, Annika H. G. Peter
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7 pages, 4 figs. Short review based on panel discussion at NAS Sackler Symposium on Dark Matter. Submitted to PNAS, to appear in Sackler Symposium proceedings
The cold dark matter (CDM) cosmological model has been remarkably successful in explaining cosmic structure over an enormous span of redshift, but it has faced persistent challenges from observations that probe the innermost regions of dark matter halos and the properties of the Milky Way's dwarf galaxy satellites. We review the current observational and theoretical status of these "small scale controversies." Cosmological simulations that incorporate only gravity and collisionless CDM predict halos with abundant substructure and central densities that are too high to match constraints from galaxy dynamics. The solution could lie in baryonic physics: recent numerical simulations and analytic models suggest that gravitational potential fluctuations tied to efficient supernova feedback can flatten the central cusps of halos in massive galaxies, and a combination of feedback and low star-formation efficiency could explain why most of the dark matter subhalos orbiting the Milky Way do not host visible galaxies. However, it is not clear that this solution can work in the lowest mass galaxies where discrepancies are observed. Alternatively, the small-scale conflicts could be evidence of more complex physics in the dark sector itself. For example, elastic scattering from strong dark matter self-interactions can alter predicted halo mass profiles, leading to good agreement with observations across a wide range of galaxy mass. Gravitational lensing and dynamical perturbations of tidal streams in the stellar halo provide evidence for an abundant population of low mass subhalos in accord with CDM predictions. These observational approaches will get more powerful over the next few years.
If cold dark matter consists of particles, these must be non-interacting and non-relativistic by definition. In most cold dark matter models however, dark matter particles inherit a non-vanishing velocity dispersion from interactions in the early universe, a velocity that redshifts with cosmic expansion but certainly remains non-zero. In this article, we place model-independent constraints on the dark matter temperature to mass ratio, whose square root determines the dark matter velocity dispersion. We only assume that dark matter particles decoupled kinetically while non-relativistic, when ga…
We constrain cold dark energy of negligible sound speed using galaxy cluster abundance observations. In contrast to standard quasi-homogeneous dark energy, negligible sound speed implies clustering of the dark energy fluid at all scales, allowing us to measure the effects of dark energy perturbations at cluster scales. We compare those models and set the stage for using non-linear information from semi-analytical modelling in cluster growth data analyses. For this, we recalibrate the halo mass function with non-linear characteristic quantities, the spherical collapse threshold and virial overd…
We explore an extended cosmological scenario where the dark matter is an admixture of cold and additional non-cold species. The mass and temperature of the non-cold dark matter particles are extracted from a number of cosmological measurements. Among others, we consider tomographic weak lensing data and Milky Way dwarf satellite galaxy counts. We also study the potential of these scenarios in alleviating the existing tensions between local measurements and Cosmic Microwave Background (CMB) estimates of the $S_8$ parameter, with $S_8=σ_8\sqrt{Ω_m}$, and of the Hubble constant $H_0$. In principl…
Recent observations in galaxies and clusters indicate dark matter density profiles exhibit core-like structures which contradict to the numerical simulation results of collisionless cold dark matter. The idea of self-interacting cold dark matter (SICDM) has been invoked to solve the discrepancies between the observations and numerical simulations. In this article, I derive some important scaling relations in galaxies and clusters by using the long-range SICDM model. These scaling relations give good agreements with the empirical fittings from observational data in galaxies and clusters if the …
In the cold dark matter scenario, dark matter halos are assembled hierarchically from smaller subunits. Some of these subunits are disrupted during the merging process, whereas others survive temporarily in the form of subhalos. A long-standing problem with this picture is that the number of subhalos predicted by simulations exceeds the number of luminous dwarf galaxies seen in the the vicinity of large galaxies like the Milky Way. Many of the subhalos must therefore have remained dark or very faint. If cold dark matter subhalos are as common as predicted, gravitational lensing may in principl…
We explore the low energy cosmological dynamics of feebly self-interacting cold dark matter and propose a new simple explanation for the rotation curves of the core-halo model in massive LSB (Low Surface brightness)galaxies. We argue in favor of the truly collisionless nature of cold dark matter,which is feebly,self-interacting at small scales between epochs of equality and recombination.For this, we assume a model, wherein strongly coupled baryon-radiation plasma ejects out of small regions of concentrated cold dark matter without losing its equilibrium. We use the Merscerskii equation i.e. t…
We allow simultaneously for a CDM--DE coupling and non--zero neutrino masses and find that significant coupling and neutrino mass are (slightly) statistically favoured in respect to a cosmology with no coupling and negligible neutrino mass (our best fits are: C~1/2m_p, m_ν~0.12eV each flavor). We assume DE to be a self--interacting scalar field and use a standard Monte Carlo Markov Chain approach.
We describe a methodology to accurately compute halo mass functions, progenitor mass functions, merger rates and merger trees in non-cold dark matter universes using a self-consistent treatment of the generalized extended Press-Schechter formalism. Our approach permits rapid exploration of the subhalo population of galactic halos in dark matter models with a variety of different particle properties or universes with rolling, truncated, or more complicated power spectra. We make detailed comparisons of analytically derived mass functions and merger histories with recent warm dark matter cosmolo…
Over the last decade, warm dark matter (WDM) has been repeatedly proposed as an alternative scenario to the standard cold dark matter (CDM) one, potentially resolving several disagreements between the CDM model and observations on small scales. Here, we reconsider the most important CDM small-scale discrepancies in the light of recent observational constraints on WDM. As a result, we find that a conventional thermal (or thermal-like) WDM cosmology with a particle mass in agreement with Lyman-$α$ is nearly indistinguishable from CDM on the relevant scales and therefore fails to alleviate any of…
The nature of dark matter is unknown. A number of dark matter candidates are quantum flavor-mixed particles but this property has never been accounted for in cosmology. Here we explore this possibility from the first principles via extensive $N$-body cosmological simulations and demonstrate that the two-component dark matter model agrees with observational data at all scales. Substantial reduction of substructure and flattening of density profiles in the centers of dark matter halos found in simulations can simultaneously resolve several outstanding puzzles of modern cosmology. The model share…
The nature of dark matter (DM) is unknown. One compelling possibility is DM being composed of primordial black holes (PBHs), given the tight limits on some types of elementary particles as DM. There is only one remaining window of masses available for PBHs to constitute the entire DM density, $10^{17} - 10^{23} \mathrm{\; g}$. Here, we show that the kernel population in the cold Kuiper belt rules out this window, arguing in favor of a particle nature for DM.
We present a new formalism to study large-scale structure in the universe. The result is a hierarchy (which we call the "Helmholtz Hierarchy") of equations describing the phase space statistics of cold dark matter (CDM). The hierarchy features a physical ordering parameter which interpolates between the Zel'dovich approximation and fully-fledged gravitational interactions. The results incorporate the effects of stream crossing. We show that the Helmholtz hierarchy is self-consistent and obeys causality to all orders. We present an interpretation of the hierarchy in terms of effective particle …
Galaxy clusters are good targets for examining our understanding of cosmology. Apart from numerical simulations and gravitational lensing, X-ray observation is the most common and conventional way to analyze the gravitational structures of galaxy clusters. Therefore, it is valuable to have simple analytical relations that can connect the observed distribution of the hot, X-ray emitting gas to the structure of the dark matter in the clusters as derived from simulations. In this article, we apply a simple framework that can analytically connect the hot gas empirical parameters with the standard …
One of possible explanations of a faint narrow emission line at 3.5 keV reported in our Galaxy, Andromeda galaxy and a number of galaxy clusters is the dark matter made of 7 keV sterile neutrinos. Another signature of such sterile neutrino dark matter could be fewer ionizing sources in the early Universe (compared to the standard "cold dark matter" (CDM) scenario), which should affect the reionization of the Universe. By using a semi-analytical model of reionization, we compare the model predictions for CDM and two different models of 7 keV sterile neutrino dark matter (consistent with the 3.5…
We consider cosmological models with dynamical dark energy (dDE) coupled to cold dark matter (CDM), while simultaneously allowing neutrinos to be massive. Using a MCMC approach, we compare these models with a wide range of cosmological data sets. We find a strong correlation between this coupling strength and the neutrino mass. This correlation persists when BAO data are included in the analysis. We add then priors on $ν$ mass from particle experiments. The claimed detection of $ν$ mass from the Heidelberg-Moscow neutrinoless double--$β$ decay experiment would imply a 7--$8 σ$ detection of CDM…
This paper has been withdrawn owing a re-arrangement of two previously submitted papers. The new version of the theoretical work on the triaxial shape of dark matter haloes can be found at the ArXiv astro-ph list (CO) as article 1104.2905
Axion as a coherently oscillating scalar field is known to behave as a cold dark matter in all cosmologically relevant scales. For conventional axion mass with 10^{-5} eV, the axion reveals a characteristic damping behavior in the evolution of density perturbations on scales smaller than the solar system size. The damping scale is inversely proportional to the square-root of the axion mass. We show that the axion mass smaller than 10^{-24} eV induces a significant damping in the baryonic density power spectrum in cosmologically relevant scales, thus deviating from the cold dark matter in the s…
We fit WMAP5 and related data by allowing for a CDM--DE coupling and non--zero neutrino masses, simultaneously. We find a significant correlation between these parameters, so that simultaneous higher coupling and ν--masses are allowed. Furthermore, models with a significant coupling and ν--mass are statistically favoured in respect to a cosmology with no coupling and negligible neutrino mass (our best fits are: C ~ 1/2m_p, m_ν~ 0.12eV per flavor). We use a standard Monte Carlo Markov Chain approach, by assuming DE to be a scalar field self--interacting through Ratra--Peebles or SUGRA potential…
Various particle physics models suggest that, besides the (nearly) cold dark matter that accounts for current observations, additional but sub-dominant dark relics might exist. These could be warm, hot, or even contribute as dark radiation. We present here a comprehensive study of two-component dark matter scenarios, where the first component is assumed to be cold, and the second is a non-cold thermal relic. Considering the cases where the non-cold dark matter species could be either a fermion or a boson, we derive consistent upper limits on the non-cold dark relic energy density for a very la…
We investigate the evolution of sub-horizon cold dark matter perturbation in the dark energy dominated era of the Universe. By generalising the Meszaros equation to be valid for an arbitrary equation of state parameter, we derive the $w$-Meszaros equation. Its solutions determine the evolution of the cold dark matter perturbation by neglecting dark energy perturbations. Our analytical results provide a qualitative understanding of this evolution.
We consider a cosmological model of the late universe constituted by standard cold dark matter plus a dark energy component with constant equation of state w and constant effective speed of sound. Neglecting fluctuations in the dark energy component we obtain an equation describing the evolution of sub-horizon cold dark matter perturbations through the epoch of dark matter-dark energy equality. We explore its analytic solutions and calculate an exact w-dependent correction for the dark matter growth function, logarithmic growth function and growth index parameter through the epoch considered. …
The electroweak axion is identified with the fuzzy dark matter of a mass $m\simeq 10^{-20}$--$10^{-19}\,{\rm eV}$. The model predicts two components of dark matter, one is ultralight and the other is WIMP-like. The Chern-Simons-type interaction between the fuzzy dark matter and photon and the $B+L$ breaking proton decays are predicted.
We consider the steady-state regime describing the density profile of a dark matter halo, if dark matter is treated as a Bose-Einstein condensate. We first solve the fluid equation for "canonical" cold dark matter, obtaining a class of density profiles which includes the Navarro-Frenk-White profile, and which diverge at the halo core. We then solve numerically the equation obtained when an additional "quantum pressure" term is included in the computation of the density profile. The solution to this latter case is finite at the halo core, possibly avoiding the "cuspy halo problem" present in so…
The Cold Spot could be an adiabatic perturbation on the surface of last scattering, in which case it is an over-density with comoving radius of the order of 1 Gpc. We assess the effect that living in a similar structure, without knowing it, has on our perception of the equation of state of Dark Energy. We find that structures of dimensions such that they could cause the Cold Spot on the CMB, affect the perceived equation of state of Dark Energy possibly up to ten percent.
We performed a series of high-resolution $N$-body simulations to examine whether dark matter candidates in the form of primordial black holes (PBHs) can solve the cusp-core problem in low-mass dwarf galaxies. If some fraction of the dark matter in low-mass dwarf galaxies consists of PBHs and the rest is cold dark matter, dynamical heating of the cold dark matter by the PBHs induces a cusp-to-core transition in the total dark matter profile. The mechanism works for PBHs in the 25-100 M$_{\sun}$ mass window, consistent with the LIGO detections, but requires a lower limit on the PBH mass fraction…
One of the open questions in modern cosmology is the small scale crisis of the cold dark matter paradigm. Increasing attention has recently been devoted to self-interacting dark matter models as a possible answer. However, solving the so-called "missing satellites" problem requires in addition the presence of an extra relativistic particle (dubbed dark radiation) scattering with dark matter in the early universe. Here we investigate the impact of different theoretical models devising dark matter dark radiation interactions on large scale cosmological observables. We use cosmic microwave backgr…
We present a thorough discussion of light dark matter produced via freeze-in in two-body decays A -> B DM. If A and B are quasi-degenerate, the dark matter particle has a cold spectrum even for keV masses. We show this explicitly by calculating the transfer function that encodes the impact on structure formation. As examples for this setup we study extended seesaw mechanisms with a spontaneously broken global U(1) symmetry, such as the inverse seesaw. The keV-scale pseudo-Goldstone dark matter particle is then naturally produced cold by the decays of the quasi-degenerate right-handed neutrinos…
We consider the rapidly-oscillating part of a $q$-field in a cosmological context and find that its energy density behaves in the same way as a cold-dark-matter component, namely proportional to the inverse cube of the cosmic scale factor.
We propose a ultraviolet complete theory for cold dark matter(CDM) and sterile neutrino that can accommodate both cosmological data and neutrino oscillation experiments at $1σ$ level. A new $U(1)_X$ dark gauge symmetry is introduced, and is assumed to be broken at $\sim \mathcal{O}$(MeV) scale. Such a light mediator for DM's self-scattering and scattering-off sterile neutrinos can resolve three controversies for cold DM on small cosmological scales, cusp vs. core, too-big-to-fail and missing satellites problems. We can also accommodate $\sim$ eV scale sterile neutrinos as the hot dark matter(H…
We perform a numerical comparison between the fuzzy dark matter model and the cold dark matter model, focusing on formation of satellite galaxy planes around massive galaxies. Such galactic dynamics with controlled initial subhalo configurations are investigated using GADGET2 for the cold dark matter and PyUltraLight for the fuzzy dark matter, respectively. We demonstrate that satellite galaxies in the fuzzy dark matter side have a tendency to form more flattened and corotating satellite systems than in the cold dark matter side mainly due to the dissipation by the gravitational cooling effect…
We review results from recent high resolution cosmological structure formation simulations, namely the Via Lactea I & II and GHALO projects. These simulations study the formation of Milky Way sized objects within a cosmological framework. We discuss the general properties of cold dark matter halos at redshift z = 0 and focus on new insights into the structure of halos we got due to the unprecedented high resolution in these simulations.
Axino arises in supersymmetric versions of axion models and is a natural candidate for cold or warm dark matter. Here we revisit axino dark matter produced thermally and non-thermally in light of recent developments. First we discuss the definition of axino relative to low energy axion one for several KSVZ and DFSZ models of the axion. Then we review and refine the computation of the dominant QCD production in order to avoid unphysical cross-sections and, depending on the model, to include production via SU(2) and U(1) interactions and Yukawa couplings.
We present a general approach for modelling the small-scale suppression in the linear matter power spectrum induced by the presence of non-cold dark matter. We show that the new parametrisation accurately describes a large variety of non-thermal scenarios, removing the need to individually test each of them. We discuss the first astrophysical constraints on its free parameters and we outline the next steps for pursuing a full statistical data analysis.
The distinctive effects of fuzzy dark matter are most visible at non-linear galactic scales. We present the first simulations of mixed fuzzy and cold dark matter, obtained with an extended version of the Nyx code. Fuzzy (or ultralight, or axion-like) dark matter dynamics are governed by the comoving Schrödinger-Poisson equation. This is evolved with a pseudospectral algorithm on the root grid, and with finite differencing at up to six levels of adaptive refinement. Cold dark matter is evolved with the existing N-body implementation in Nyx. We present the first investigations of spherical colla…
Astrophysics gives evidence for the existence of Dark Matter and puts constraints on its nature. The Cold Dark Matter model has become "standard" cosmology combined with a cosmological constant. There are indications that "Cold" Dark Matter could be "warmer" than initially discussed. This paper reviews the main information on the Cold/Warm nature of Dark Matter.
We explore ways of creating cold keV-scale dark matter by means of decays and scatterings. The main observation is that certain thermal freeze-in processes can lead to a cold dark matter distribution in regions with small available phase space. In this way the free-streaming length of keV particles can be suppressed without decoupling them too much from the Standard Model. In all cases, dark matter needs to be produced together with a heavy particle that carries away most of the initial momentum. For decays, this simply requires an off-diagonal DM coupling to two heavy particles; for scatterin…
The presence of a hot dark matter component has been hinted at 3 sigma by a combination of the results from different cosmological observations. We examine a possibility that pseudo Nambu-Goldstone bosons account for both hot and cold dark matter components. We show that the QCD axions can do the job for the axion decay constant f_a < O(10^10) GeV, if they are produced by the saxion decay and the domain wall annihilation. We also investigate the cases of thermal QCD axions, pseudo Nambu-Goldstone bosons coupled to the standard model sector through the Higgs portal, and axions produced by modul…
Structure formation creates high temperature and density regions in the Universe that allow the conversion of matter into more stable states, with a corresponding emission of relativistic matter and radiation. An example of such a mechanism is the supernova event, that releases relativistic neutrinos corresponding to 99% of the binding energy of remnant neutron star. We take this phenomena as a starting point for an assumption that similar processes could occur in the dark sector, where structure formation would generate a late time conversion of cold dark matter into a relativistic form of da…
With an aim to argue for the truly collisionless nature of cold dark matter between epochs of equality and recombination, we assume a model, wherein strongly coupled baryon-radiation plasma ejects out of small regions of concentrated cold dark matter without losing its equilibrium. We use the Meschersky equation to describe the dynamics of cold dark matter in the presence of varying mass of strongly coupled baryon-radiation plasma. Based on this model, we discuss the growth of perturbations in cold dark matter both in the Jeans theory and in the expanding universe using Newton's theory. We see…
We provide a holographic dual description of Milgrom's scaling associated with galactic rotation curves. Our argument is based on the recent entropic reinterpretation of Newton's laws of motion. We propose a duality between cold dark matter and modified Newtonian dynamics (MOND). We introduce the concept of MONDian dark matter, and discuss some of its phenomenological implications. At cluster as well as cosmological scales, the MONDian dark matter would behave as cold dark matter, but at the galactic scale, the MONDian dark matter would act as MOND.
Cold dark matter axions form a Bose-Einstein condensate if the axions thermalize. Recently, it was found that they do thermalize when the photon temperature reaches T ~ 100 eV(f/10^12GeV)^1/2 and that they continue to do so thereafter. We discuss the differences between axion BEC and CDM in the linear regime and the non-linear regime of evolution of density perturbations. We find that axion BEC provides a mechanism for the production of net overall rotation in dark matter halos, and for the alignment of cosmic microwave anisotropy multi-poles.
We study the parameter space of cold dark matter axions in two cosmological scenarios with non-standard thermal histories before Big Bang nucleosynthesis: the Low Temperature Reheating (LTR) cosmology and the kination cosmology. If the Peccei-Quinn symmetry breaks during inflation, we find more allowed parameter space in the LTR cosmology than in the standard cosmology and less in the kination cosmology. On the contrary, if the Peccei-Quinn symmetry breaks after inflation, the Peccei-Quinn scale is orders of magnitude higher than standard in the LTR cosmology and lower in the kination cosmolog…
We propose a decaying cold dark matter model to explain the excess of electron recoil observed at the XENON1T experiment. In this scenario, the daughter dark matter from the parent dark matter decay easily obtains velocity large enough to saturate the peak of the electron recoil energy around 2.5 keV, and the observed signal rate can be fulfilled by the parent dark matter with a mass of order 10-200 MeV and a lifetime larger than the age of Universe. We verify that this model is consistent with experimental limits from dark matter detections, Cosmic Microwave Background and Large Scale Structu…
The subjects of this thesis are the invisible axion and the more general family of axion-like particles. The invisible axion is a hypothetical elementary particle and a cold dark matter candidate. I present an improved computation of the constraints on the parameter space of the cold dark matter axion in the standard cosmology, that includes the contributions from anharmonicities in the axion potential and from the decay of axionic strings. In this scenario, I update the value of the mass of the cold dark matter axion, finding the value $(67\pm17){\rm μeV}$, approximately one order of magnitud…
In usual particle models, sterile neutrinos can account for the dark matter of the Universe only if they have masses in the keV range and are warm dark matter. Stringent cosmological and astrophysical bounds, in particular imposed by X-ray observations, apply to them. We point out that in a particular variation of the inert doublet model, sterile neutrinos can account for the dark matter in the Universe and may be either cold or warm dark matter candidates, even for masses much larger than the keV range. These Inert-Sterile neutrinos, produced non-thermally in the early Universe, would be stab…
Dwarf spheroidal galaxies provide well-known challenges to the standard cold and collisionless dark matter scenario: The too-big-to-fail problem, namely the mismatch between the observed mass enclosed within the half-light radius of dwarf spheroidals and cold dark matter N-body predictions; The hints for inner constant-density cores. While these controversies may be alleviated by baryonic physics and environmental effects, revisiting the standard lore of cold and collisionless dark matter remains an intriguing possibility. Self-interacting dark matter may be the successful proposal to such a s…
We study the effects of cold dark matter on the propagation of gravitational waves of astrophysical and primordial origin. We show that the dominant effect of cold dark matter on gravitational waves from astrophysical sources is a small frequency dependent modification of the propagation speed of gravitational waves. However, the magnitude of the effect is too small to be detected in the near future. We furthermore show that the spectrum of primordial gravitational waves in principle contains detailed information about the properties of dark matter. However, depending on the wavelength, the ef…
Many models of dark matter contain more than one new particle beyond those in the Standard Model. Often heavier particles decay into the lightest dark matter particle as the Universe evolves. Here we explore the possibilities that arise if one of the products in a (Heavy Particle) $\rightarrow$ (Dark Matter) decay is a positron, and the lifetime is shorter than the age of the Universe. The positrons cool down by scattering off the cosmic microwave background and eventually annihilate when they fall into Galactic potential wells. The resulting 511 keV flux not only places constraints on this cl…
By eschewing finetuning from the electroweak and QCD sectors of supersymmetry (natural supersymmetry or SUSY), and by invoking the Kim-Nilles solution to the SUSY mu problem, one is lead to models wherein the dark matter is comprised of a mixture of axions and higgsino-like WIMPs. Over a large range of Peccei-Quinn breaking scale f_a~ 10^9-10^{12} GeV, one then expects about 90-95% axion dark matter. In such a scenario, both axion and WIMP direct detection may be expected.
We show that for a relatively light majoron ($\ll 100 $ eV) non-thermal production from topological defects is an efficient production mechanism. Taking the type I seesaw as benchmark scheme, we estimate the primordial majoron abundance and determine the required parameter choices where it can account for the observed cosmological dark matter. The latter is consistent with the scale of unification. Possible direct detection of light majorons with future experiments such as PTOLEMY and the formation of boson stars from the majoron dark matter are also discussed.
We propose a new framework unifying cold dark matter (CDM) and Modified Newtonian Dynamics (MOND) to solve their respective problems on galactic scales and large scale structure formation. In our framework the dark matter clusters on large scales but not on galactic scales. This environment dependence of the dark matter behaviors is controlled by a vector field, which also produces the MOND effects in galaxies. We find that in this framework only a single mass scale needs to be introduced to produce the phenomena of CDM, MOND and also dark energy.
We study the conditions for the adiabatic resonant conversion of the cold dark matter (CDM) axions into photons in existence of the astrophysically sourced strong magnetic fields such as those in the neutron star magnetosphere. We demonstrate the possibility that the forthcoming radio telescopes such as the SKA (Square Kilometre Array) can probe those photon signals from the CDM axions.
We show that hidden hot dark matter, hidden-sector dark matter with interactions that decouple when it is relativistic, is a viable dark matter candidate provided it has never been in thermal equilibrium with the particles of the standard model. This hidden hot dark matter may reheat to a lower temperature and number density than the visible Universe and thus account, simply with its thermal abundance, for all the dark matter in the Universe while evading the typical constraints on hot dark matter arising from structure formation. We find masses ranging from ~3 keV to ~10 TeV. While never in e…
We examine the evolution of non-relativistic cold dark matter gravitationally coupled to baryons with modes deep inside the Hubble radius (sub-horizon regime) using akinetic theory approach within the realm of Newtonian theory. We obtain the general solution for the total density perturbation and we also show that a baryon perturbation catches up with the dark matter perturbation at late times, which in turn makes possible the formation of bound structures. We extend the linear perturbation analysis by considering the turn-around event, the collapse of matter, and its virialization process.
